Quantum compiler optimizations:
The state-of-the-art quantum compilers [1]}, [2]} usually have multiple passes to execute different optimizations, (e.g., circuit rewriting [3]}, gate cancellation [4]}, template matching [5]}, qubit mapping [6]}).
These passes applied on the low-level gate sequences usually only rewrite the circuit locally on very few qubits or gates every time and only focus on one optimization objective in each pass.
Different from these optimizations, all passes in Paulihedral performance program transformations at a much larger scope in a scalable way and multiple optimization opportunities can be reconciled because the high-level algorithmic information is leveraged.
This makes Paulihedral optimizations more effective than simply combining those small-scale single-objective passes.
